While I haven't studied the subject, I did a bit of looking and found some information from the Prose Edda which seems to qualify as a primary source (written around 1220). In any case, according to it, "all those who fall in battle are [Odin's] adopted sons" and are known as Einherjar. This includes "all those men that have fallen in battle since the beginning of the world".
So if you go by that, then the only requirement is that you must die in battle. Depending on interpretation, this might require the candidate to die fighting (because if they were fleeing or were a noncombatant, then they might not themselves be "in battle" despite dying on a battlefield due to a battle). No requirement for skill, or overt levels of heroism, cultural background, etc. (There is mention of oaths sworn to Odin, so I assume there's an opt-out clause for those who choose not to join up, which might weed out those who don't like to fight enough that they want to continue fighting until the end of the world.)
I guess it depends on how you define the Einherjar at your table.